Prati Sarg of Bhavishya Puraan also give the account of future kings, or kings in Kali Yug.

Future Kings in Kuru Vansh

Paraashar Jee said - "Hey Maitreya Jee, Now I tell you about the future kings [of this Chandra Vansh, or Puru Vaysh, or Kuru Vansh] The present king Pareekshit will have four sons - Janamejaya, Shrutsen, Ugrasen and Bheemsen.

Janamejaya's son will be Shataaneek who will study Ved from Yaagyavalkya, learn weapons from
    Kripaa and will get Parampad hearing discourses from Shaunak Jee
Shataaneek's son will be Ashwameghdatt
Ashwameghdatt's son will be Adhiseemkrishn
Adhiseemkrishn's son will be Nichakru who will live in Kaushaambee Puree after Gangaa will have
    flowed away Hastinaapur
Nichakru's son will be Ushn
Ushn's son will be Vichitrarath
Vichitrarath's son will be Shuchirath
Shuchirath's son will be Vrishnimaan
Vrishnimaan's son will be Sushen
Sushen's son will be Suneeth
Suneeth's son will be Nrip

Nrip's son will be Chakshu
Chakshu's son will be Sukhaaval
Sukhaaval's son will be Paariplav
Paariplav's son will be Sunaya
Sunaya's son will be Medhaavee
Medhaavee's son will be Ripunjaya
Ripunjaya's son will be Mridu
Mridu's son will be Tigm
Tigm's son will be Brihdrath
Brihdrath's son will be Vasudaan
Vasudaan's son will be Shataaneek
Shataaneek's son will be Udayan
Udayan's son will be Aheenar
Aheenar's son will be Dandpaani
Dandpaani's son will be Niramitra
Niramitra's son will be Kshemak

In this regard this Shlok is said - "Which Vansh is the cause of Braahman and Kshatriya, that Vansh will end here with the birth of Kshemak."

Future Ikshwaaku Kings

Paraashar Jee said - "Now I tell you the future kings of Ikshwaaku Vansh. (Onward from Brihadwal)

Brihadwal's son will be Brihatkshan
Brihatkshan's son will be Urukshaya
Urukshaya's son will be Vatsavyooh
Vatsavyooh's son will be Prativyom
Prativyom's son will be Divaakar
Divaakar's son will be Sahadev
Sahadev's son will be Brihadashwa
Brihadashwa's son will be Bhaanurath
Bhaanurath's son will be Prateetaashwa
Prateetaashwa's son will be Suprateek
Suprateek's son will be Marudev
Marudev's son will beSunakshatra
Sunakshatra's son will be Kinnar

Kinnar's son will be Antariksh
Antariksh's son will be Suparn
Suparn's son will be Amitrajit
Amitrajit's son will be Brihadraaj
Brihadraaj's son will be Dharmee
Dharmee's son will Kritanjaya
Kritanjaya's son will be Rananjaya
Rananjaya's son will be Sanjaya
Sanjaya's son will be Shaakya
Shaakya's son will be Shuddhodan
Shuddhodan's son will be Rahul
Rahul's son will be Prasenjit
Prasenjit's son will be Kshudrak
Kshudrak's son will be Kundak
Kundak's son will be Surath
Surath's son will be Sumitra

This Vansh will end with the birth of Sumitra in Kali Yug.

Future Magadh Vansh

Paraashar Jee said - "Now I tell you about Magadh Vansh. In this Vansh Jaraasandh etc kings were main.   Continues from 

Jaraasandh's son is Sahadev
Sahadev's son is Somaapi
Somaapi's son will be Shrutshravaa
Shrutshravaa's son will be Ayutaayu
Ayutaayu's son will be Naramitra
Naramitra's son will be Sunetra
Sunetra's son will be Brihatkarmaa
Brihatkarmaa's son will be Senjit
Senjit's son will be Shrutanjaya
Shrutanjaya's son will be Vipra

Vipra's son will be Shuchi
Shuchi's son will be Kshemya
Kshemya's son will be Suvrat
Suvrat's son will be Dharm
Dharm's son will be Sushravaa
Sushravaa's son will be Dridhsen
Dridhsen's son will be Subal
Subal's son will be Suneet
Suneet's son will be Satyajit
Satyajit's son will be Vishwajit
Vishwajit's son will be Ripunjaya

Here ends this Brihadrath's descendents. They will rule up to 1,000 years.